In the mathematics curriculum standard, we found a sentence-"Let students experience the process of abstracting practical problems into mathematical models and explaining and applying them, so that students can gain an understanding of mathematics and make progress and development in their thinking ability, emotional attitude and values." In fact, it is required to regard the process of students learning mathematical knowledge as the process of establishing mathematical model, cultivate students' awareness of mathematical application in the process of modeling, and guide students to consciously analyze and solve problems in life by mathematical methods. It is clearly required that teachers guide students to establish mathematical models in teaching, not only focusing on the results, but also on the process of students' independent establishment of mathematical models, so that students can establish mathematical models scientifically, reasonably and effectively in the process of inquiry learning.

First, the concept of mathematical model

A mathematical model is a mathematical structure that summarizes or approximates the characteristics or quantitative dependence of a certain thing system. All kinds of concepts, formulas and theories in mathematics are abstracted from the prototype of the real world. In this sense, all mathematical knowledge is a model to describe the real world. In a narrow sense, a mathematical model refers to a mathematical relationship structure that reflects a specific problem or a specific thing system, and is a mathematical expression of variables and their relationships in the corresponding system. Mathematical modeling is a method of establishing mathematical models to solve problems. Mathematics curriculum standard arranges four learning fields: number and algebra, space and graphics, statistics and probability, practice and comprehensive application, which emphasizes students' mathematical activities and develops students' sense of number, symbol, space, application and reasoning ability. The most important part of these contents is the mathematical model. In the primary school stage, mathematical models are represented by a series of concept systems, algorithm systems, relationships, laws, axiomatic systems and so on.

Second, the feasibility of infiltrating mathematical modeling ideas into primary school mathematics teaching

Mathematical model not only provides an effective way for mathematical expression and communication, but also provides an important tool for solving practical problems, which can help students understand and understand the meaning of mathematics accurately and clearly. In primary school mathematics teaching activities, teachers should take effective measures to strengthen the infiltration of mathematical modeling ideas, improve students' interest in learning, and cultivate students' awareness of using mathematics and their ability to analyze and solve practical problems. In essence, mathematics develops and enriches in the process of abstraction, generalization and modeling. Mathematics learning is the real mathematics learning only if it goes deep into the meaning of "model" and "modeling". This kind of "in-depth", as far as primary school mathematics teaching is concerned, refers to guiding mathematics teaching with the idea and spirit of mathematical modeling. "Starting from students' existing life experience, let students experience the process of abstracting practical problems into mathematical models and explaining and applying them, so that students can gain an understanding of mathematics, and at the same time gain entry and development in many aspects such as thinking ability, emotional attitude and values. "

Third, how do primary school students form their own mathematical modeling?

Mathematics comes from life and serves life. Therefore, it is necessary to introduce materials related to mathematics learning in real life into the classroom in time, describe the background of mathematics problems through familiar examples in life, and show the contents of teaching materials to students in a situational way in the classroom. The creation of scenarios should be combined with the reality of social life, hot issues of the times, nature, social culture and other factors related to mathematical problems, so that students can feel real, novel, interesting and operable, and meet their curious and active psychological requirements. It is easy to stimulate students' interest, activate the existing life experience in their minds, and make students feel hidden mathematical problems with accumulated experience, thus prompting students to abstract life problems into mathematical problems and perceive the existence of mathematical models.

Fourth, participate in inquiry and actively build mathematical models.

Mathematician Hua summed up through years of study and research experience: we should not only remember the conclusion, understand some principles, laws and formulas in books, but also imagine how others came up with it and how it was refined step by step. Only through such a process of exploration can the ideas and methods of mathematics be precipitated and condensed, thus making knowledge have greater wisdom value. Hands-on practice, independent exploration and cooperative communication are important ways for students to learn mathematics. Students' mathematics learning activities should be a positive, lively, vivid and personalized process. Therefore, in teaching, we should be good at guiding students to explore independently, cooperate and communicate, actively summarize and improve the learning process, learning materials and learning findings, and strive to build a mathematical model that everyone can understand.

The teacher provided students with several empty boxes, sand and other learning tools, such as cylinders, cuboids, cubes and cones (in which cylinders and cones have equal base height relations, but not equal base height relations, and cones and other shapes have no equal base height relations), and the students started the experiment in groups.

In the above-mentioned teaching process, teachers provide a wealth of experimental materials, from which students need to choose the materials needed to solve problems for research. Students' problems cannot be solved in one step. Through the process of guessing, verifying, modifying the experimental scheme, guessing and verifying again, students gradually transition to a complex and more general situation. In the process of active exploration and attempt, students carry out re-creation learning and independently summarize the formula for calculating the volume of a cone in an abstract way. The design of this link not only develops students' strategic knowledge, but also allows students to experience the mathematical thinking process of guessing, verifying, analyzing and summarizing, and abstracting. In the process of learning, students sometimes think independently, sometimes study in groups, and sometimes combine independent exploration with cooperative learning. Students fully experience the formation process of mathematical model in the exploration of new knowledge.

Fifth, solve problems and expand the application of mathematical models.

Use the established mathematical model to answer the questions in real life and let students understand the mathematical model.